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Keywords
(15)
Analytic Function
Anderson Model
Counting Function
Eigenvalues
eigenvalues and eigenfunctions
Hamiltonian Matrix
Linear Algebra
Matrix Algebra
Numerical Analysis
Numerical Linear Algebra
Random Potential
Recursion Relation
Transfer Matrix
Tridiagonal Matrix
Tight Binding
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Counting the exponents of single transfer matrices
Counting the exponents of single transfer matrices,10.1063/1.3594654,Luca Guido Molinari,Giuseppe Lacagnina
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Counting the exponents of single transfer matrices
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Luca Guido Molinari
,
Giuseppe Lacagnina
The eigenvalue equation of a band or a block tridiagonal matrix, the
tight binding
model for a crystal, a molecule, or a particle in a lattice with
random potential
or hopping amplitudes, and other problems lead to threeterm recursive relations for (multicomponent) amplitudes. Amplitudes n steps apart are linearly related by a transfer matrix, which is the product of n matrices. Its exponents describe the decay lengths of the amplitudes. A formula is obtained for the
counting function
of the exponents, based on a duality relation and the Argument Principle for the zeros of analytic functions. It involves the corner blocks of the inverse of the associated Hamiltonian matrix. As an illustration, numerical evaluations of the
counting function
of quasi 1D
Anderson model
are shown.
Published in 2011.
DOI:
10.1063/1.3594654
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References
(18)
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